@Vettie10 

Hi,

Since you say you've just purchased the range extender I assume it must be one of the more recent models. Can you maybe post the model number of it?

Yes, the e-mail and password of the account for this forum can be used to log into the Tether app. But logging into the Tether app doesn't require an actual TP-Link product. 
So, if you can't even log into the Tether app, then this is not related to the range extender at all.

Obviously, the Tether app will require an active connection to the Internet to be able to authenticate you. 

Have you maybe set up an overly complicated and long password for your TP-Link account? If yes, then log into the TP-Link forum, change it to something more usual and then try again to log into the Tether app with your credentials.

Once you have managed to log into the Tether app connect the Wi-Fi of the phone or tablet to the SSID of the range extender (something like "TP-Link_Extender") and then the Tether app should find it and show it with its model number. When you tap on the device and given the device is brand new or freshly factory-reset, then Tether should ask you to setup an administrator password for this device. It is important to remember this password, because it might be needed again in the future.